Simplify. Remove all perfect squares from inside the square roots. Assume $a$ and $b$ are positive. $\sqrt{42a^4b^6}=$
Answer: $\begin{aligned} \sqrt{42a^4b^6}&=\sqrt{\left(a^2\right)^2\cdot \left(b^3\right)^2\cdot 2 \cdot 3 \cdot 7} \\\\ &=\sqrt{\left(a^2\right)^2}\cdot\sqrt{\left(b^3\right)^2}\cdot\sqrt{42} \\\\ &=a^2\cdot b^3\cdot\sqrt{42} \\\\ &=a^2b^3\sqrt{42} \end{aligned}$ In conclusion, $\sqrt{42a^4b^6}=a^2b^3\sqrt{42}$